Prof
Robert Goldstone from Indiana University is visiting the UoN School of
Psychology, and will give a seminar this Thur, April 6, 12-1pm, Keats room. Please find the title and abstract below.
Prof
Goldstone is Distinguished Professor in the Psychological and Brain Sciences
department and Cognitive Science program at Indiana University. His research
interests include concept learning and representation, perceptual learning,
educational applications of cognitive science, decision making, collective
behavior, and computational modeling of human cognition.
Mathematical Reasoning as a Literally Physical Symbol
System
Robert Goldstone
Indiana University, Department of Psychological and
Brain Science and Program in Cognitive Science
Much
of the power of mathematics comes from its generality and ability to
unify prime face dissimilar domains. The same
combinatorics formula applies to sealing wax, cabbages, and kings with no
customization needed, or even permitted. By one account, analytic
thought in math and science requires developing deep construals of phenomena
that run counter to untutored perceptions. This approach draws an
opposition between superficial perception and principled
understanding. In this talk, I advocate the converse strategy of
grounding mathematical reasoning in perception and action. I will
describe empirical evidence for perceptual changes that accompany learning in
mathematics. In arithmetic and algebraic reasoning, we find that
proficiency involves executing spatially explicit transformations to notational
elements. People learn to attend mathematical operations in the
order in which they should be executed, and the extent to which students employ
their perceptual attention in this manner is positively correlated with their
mathematical experience. People produce mathematical notations that
they are good at reading. Perception, attention, and action routines
are tailored to fit mathematical requirements. Thus, for reasoning
in mathematics (and science, but that’s another talk), relatively sophisticated
performance can be achieved not only by ignoring perceptual features in favor
of deep conceptual features, but also by adapting perceptual processing so as
to conform with and support formally sanctioned responses. These
“Rigged Up Perception and Action Systems” (RUPAS) offer a promising general
strategy for achieving educational reform. Based on the theoretical foundation
of RUPAS, we have begun to design, implement, and assess virtual, interactive
sandboxes for students to explore algebra.
